Welcome to FT, Tweety!!!

Google says this can be driven in 8 1/2 hours. It also says that driving to Norfolk takes 1 1/2 hours. As a first time flyer you will probably try to arrive at the airport 2 hours in advance. Add those times up, and you could practically have already driven halfway to Chattanooga!

Given that you are going to need a rental car in TN, how about renting a car with unlimited mileage in Richmond and driving to Chattanooga and then driving back? By renting a car in Richmond, you put the miles on the rented car, not your own. If you get an economy car, even counting gas, you might well save a bit of money and can come and go on your own schedule.